A raindrop of mass 1 g starts from rest at a height of 1 km above the ground. It reaches the ground with a speed of 5 m·s⁻¹. Taking g = 10 m·s⁻², what is the work done by the unknown resistive force during the fall?
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Question

A raindrop of mass 1 g starts from rest at a height of 1 km above the ground. It reaches the ground with a speed of 5 m·s⁻¹. Taking g = 10 m·s⁻², what is the work done by the unknown resistive force during the fall?

Options

G1 Physics · Accepted Answer

Use the work-energy theorem. Work done by gravity + work done by the resistive force = change in kinetic energy. Thus, mgh + W(res) = (1 ÷ 2)mv². Therefore, W(res) = (1 ÷ 2)mv² - mgh. Here, m = 1 g = 10⁻³ kg, h = 1000 m, v = 5 m·s⁻¹. So, W(res) = (1 ÷ 2)(10⁻³)(25) - (10⁻³)(10)(1000) = 0.0125 - 10 = -9.9875 J. The source answer key marks option D, -9.98 J. The exact value from the stated data is -9.9875 J. Correct option: D.